Spatial Fluctuations of the Density of States in Magnetic Fields Observed with Scanning Tunneling Spectroscopy

Scanning tunneling spectroscopy images on $n-\mathrm{InAs}\left(110\right)$ exhibit a strong magnetic field dependent contrast on the 50 nm length scale, indicating fluctuations in the density of states of the sample. The contrast is correlated to previously observed Landau oscillations in $\mathrm{dI}/\mathrm{dV}$ curves. Its origin is a spatial fluctuation of the Landau level energy of 3–4 meV caused by the inhomogeneous distribution of dopant atoms. Besides inducing large-scale fluctuations in the density of states, dopants preserve their ability to scatter electron waves. The resulting wave pattern is found to depend on the magnetic field. It is suggested that the dependence is guided by the condensation of the electronic states on Landau tubes.